06 Dose
Water-to-air stopping-power ratio
Teaching fit: (s/ρ)_w,air ≈ 1.102 + 0.003 × (10 − TPR20,10)×10 for MV photons (order of magnitude).
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Simulation
Water-to-air stopping-power ratio — Change the numbers; the scene follows.
Where it works
Water phantom
Ion chamber
In the water tank under the linac, at the ion chamber — reference dosimetry happens here.
Open this machineFormula
Variables
Results
(s/ρ)_w,air
Stopping-power ratio
1.0995
Explanation
What it means
The Spencer–Attix water/air stopping-power ratio falls slowly as the beam hardens (more forward, higher-energy secondaries). Co-60 ≈ 1.133, 6 MV ≈ 1.127, 18 MV ≈ 1.100. This linear teaching fit around TPR20,10 is for intuition — clinical kQ tables already fold SPR, μen and perturbations together. Electrons have a separate, depth-dependent SPR. This is a working relation in Dosimetry.
Where it is used
Clinically it sits on the Water phantom — Ion chamber. In the water tank under the linac, at the ion chamber — reference dosimetry happens here. Dosimetry is the chamber in water under the linac, or the well counter in the hot lab: TG-51, TRS-398, kerma, and recombination. These numbers are the calibration the rest of the department borrows.
Water phantom · Open this machineHow to use it
Enter TPR20,10 (0.57 Co-60-like, 0.67 6 MV, 0.77 18 MV). Read the teaching SPR. Compare with the value in TRS-398 Table I for your chamber, which will differ because of the other factors inside kQ. Change one input and watch the curve and the simulation follow.
Symbols
- TPR20,10Quality index0.67
Worked example
A typical case from the default values: TPR20,10 = 0.67 (Quality index). Substituting into the relation gives (s/ρ)_w,air = 1.0995. These are teaching numbers — align them with your machine.
Typical values give
- (s/ρ)_w,air = 1.0995
Where it comes from
The displayed formula is the working relation. Teaching fit: (s/ρ)_w,air ≈ 1.102 + 0.003 × (10 − TPR20,10)×10 for MV photons (order of magnitude). Usual reference: Andreo / TRS-398 (fit for teaching). Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Andreo / TRS-398 (fit for teaching)
Assumptions & limits
Fit, not a Monte Carlo. Valid-ish 0.55–0.80 TPR. Do not use for electrons, kV, or protons (ICRU 78 / TRS-398 proton has its own s_w,air). Never multiply this SPR onto a TG-51 D_w that already includes it.
Pitfalls
kQ is for that chamber and that beam quality — not a neighbour's value. Polarity and recombination are measured, not copied. A ⁶⁰Co N_D,w is not an MV calibration until kQ is applied. Fit, not a Monte Carlo. Valid-ish 0.55–0.80 TPR. Do not use for electrons, kV, or protons (ICRU 78 / TRS-398 proton has its own s_w,air). Never multiply this SPR onto a TG-51 D_w that already includes it.
Keep this
Trace every gray back to a protocol, a chamber, and a quality index. Fit, not a Monte Carlo. Valid-ish 0.55–0.80 TPR. Do not use for electrons, kV, or protons (ICRU 78 / TRS-398 proton has its own s_w,air). Never multiply this SPR onto a TG-51 D_w that already includes it.
In this specialty